SCANNING VOL. 21, 368–371 (1999) Received August 13, 1999© FAMS, Inc. Accepted September 15, 1999

Comparison of Different Models for the Generation of ElectronBackscattering Patterns in the Scanning Electron Microscope

OLIVER C. WELLS

IBM Research Division, Yorktown Heights, New York, USA

Summary: An electron backscattering pattern (EBSP) isformed on a fluorescent (or other) screen from the fasterscattered electrons when a single-crystal region of a solidsample is illuminated by a finely focused electron beam(EB). The EBSP is very similar in appearance to the elec-tron channeling pattern (ECP) that is obtained in the scan-ning electron microscope (SEM) by rocking the beamabout a point on the surface of a single crystal. It has beensuggested that the mechanisms that give rise to EBSP andECP are related by reciprocity. If this is indeed the case,then the models that are used to explain them should be thesame except for the direction in which the electrons travelthrough the specimen. The two-event “diffraction model”for EBSP (diffuse scattering followed by diffraction) failsthis condition, leading to the conclusion that the “chan-neling in and channeling out” model for EBSP is morelikely to be correct. This has been described rigorously byReimer (1979, 1985). It is named after the title used by Joy(1994). An attempt is made here to describe this model ina simple way.

Key words: Bloch waves, electron backscattering pat-terns, electron channeling patterns, electron channeling,electron diffraction, scanning electron microscopy, wide-angle scattering event

Introduction

The purpose of this article is to argue in favor of the“channeling in and channeling out” model for the forma-tion of electron backscattering patterns (EBSP) in the scan-ning electron microscope (SEM). This was described rig-orously by Reimer (1979, 1985). It is named after the titleused by Joy (1994).

An EBSP is formed when a finely focused electronbeam (EB) is incident onto a tilted single-crystal target

(Alam et al. 1954, Dingley et al. 1995, Reimer et al. 1986).The faster scattered electrons land on a recording screen togive a pattern of lines and bands of contrast related to thecrystal structure (Fig. 1a).

Closely related to the EBSP (and very similar in appear-ance to it) is the electron channeling pattern (ECP) (Bookeret al. 1967; Coates 1967; Joy et al. 1982). Here, an EB isrocked about a point on the surface of a single crystal (Fig.1b). Either the backscattered electrons (BSE) or the sec-ondary electrons (SE) are collected and used to modulate thebrightness of a cathode ray tube (or other form of display)scanned in sympathy with the incident angle of the EB. Theformation of electron channeling patterns (ECP) is generallyexplained in terms of Bloch waves as described below.

Venables and Harland (1974) wrote: “It is fairly clear...that E.B.S.P.s and E.C.P.s are related theoretically by thereciprocity theorem.” The explanations for EBSP and ECPshould therefore be the same, except for the direction inwhich the electrons travel through the specimen (Fig. 1).

In the past, the EBSP has been explained by the samemodel as for Kikuchi lines in the transmission electronmicroscope (TEM). Thus, Alam et al. (1954) wrote:

“The electrons are first assumed to be diffused in thecrystal (by an unspecified scattering process) and thento be reflected by a set of Bragg planes. . . The bands aretermed “excess” or “defect” according to whether theintensity in the band is greater or less than the averageintensity in the neighbourhood of the band.”

Here, this model is referred to as the two-event “diffractionmodel” for EBSP (Fig. 2a).

It is argued here (based on reciprocity) that for EBSP thediffuse scattering and diffraction events described above astaking place separately (A and B in Fig. 2a) are in fact soclosely related that it is more realistic to regard the EBSPas being formed by the “channeling in and channeling out”model in which the channeling processes modulate theprobability of a wide-angle scattering event C as shown inFigure 2b. This is discussed in more detail below.

The basic processes that give rise to EBSP and ECP wereinvestigated in the first instance with reference to extinc-tion contours of single-crystal thin foils in the TEM(Hashimoto et al. 1962). That is to say, the transmitted elec-trons are absorbed more strongly when the electrons pass

Address for reprints:

Oliver C. Wells, 20-206Research Staff Member EmeritusIBM Research Division, Box 218Yorktown Heights, NY 10598, USA

through the films on one side of the Bragg reflecting angle.Hirsch et al. (1962) predicted that the probability of gen-erating an x-ray will be greater under the high-absorptioncondition. Duncumb (1962) verified experimentally witha thin gold foil that this was indeed the case for x-rays, SE,and BSE. Thus, many types of scattering are enhancedunder these conditions.

In this discussion, the expression “wide-angle scatteringevent” is understood to refer to any wide-angle scatteringevent with essentially no loss of energy at an atomicnucleus. No distinction is made here between the Ruther-ford, Mott, phonon, or any other description of this process.

Explanation of Electron Channeling Patterns inTerms of Bloch Waves

Here, a parallel incident EB rocks relative to the inputBragg planes and, after a short penetration into the crys-tal, is scattered by a wide-angle event toward the detector.This involves a very close interaction between the way inwhich the incident electrons are expressed in terms ofBloch waves and the probability of a wide-angle scatter-ing event.

Booker (1970) described Bloch waves as follows:

“When an electron beam is incident on a crystal at aBragg reflecting position, the electrons scattered withinthe crystal only reinforce in two directions, the incidentbeam direction and the Bragg diffracted beam direction.These directions are separated by 2θ, where θ is theBragg angle, typically 1 or 2 degrees for 20 keV elec-trons. Electrons are continually scattered from the directbeam to the diffracted beam and back again, and theamplitudes of both beams vary in a periodic manner withdepth in the crystal. However, if the two beams are con-sidered together, the electrons move on average parallelto the Bragg atomic planes, and the amplitude of thiscombined wave, termed a Bloch wave, does not vary ina periodic manner with depth.”

The Bloch wave has a double significance. First, it is theelectron wave in the crystal. Second, if the electron is tobe regarded as being a particle, then the square of theamplitude of the Bloch wave gives the probability that theparticle will be found at that point. (Thus, the amplitudeof the Bloch wave at an atomic nucleus will determine theprobability of wide-angle scattering at that point.) The factthat the Bloch wave moves in a direction parallel to theBragg planes while the incident EB is close to the Braggdirection is the reason why this process is referred to as“channeling.”

The formation of ECP follows from the fact that the posi-tion of the peaks of the Bloch waves relative to the atomicplanes will depend on the incident direction of the electronsrelative to the Bragg planes. In agreement with the mostrecent terminology, Figure 3a shows a type-1 Bloch wave

O.C. Wells: Electron backscattering patterns 369

with maxima along the lines of atom centers, while for thetype-2 wave shown in Figure 3b the maxima are mid-waybetween these planes. Electrons that are incident at the pre-cise Bragg angle can be expressed as a combination of type-1 and type-2 waves of equal amplitude. For incident elec-tron directions that are closer to the atomic planes, theamplitude of the type-1 wave is greater, so the probabilityof wide-angle scattering is increased. For incident anglesgreater than the Bragg angle, the reverse applies.

To summarize the formation of ECP by considering thecontinuous scattering back and forth between the directbeam and the diffracted beam during the initial stages of elec-tron penetration, it is found that the strength of the electronwave along the atomic planes will depend upon the direc-tion of the incident electrons relative to the Bragg planes.This in turn affects the probability of wide-angle scatteringsuch as gives rise to the signal when generating an ECP.

This process must be reversed to give rise to EBSP. Onething is certain: the Bloch waves in the input Bragg planesin the ECP are very closely involved in controlling the prob-ability of the wide-angle scattering event (Fig. 1b). In thesame way, when the directions of the electron paths arereversed as in Figure 1a to give an EBSP, then the very closerelationship between these two processes suggests that itis incorrect to think of two separate events, and that thesemust be combined in some way into a single process.

FIG. 1 Reciprocal relationship between (a) electron backscatteringpatterns, (b) ECP based on Venables and Harland (1974) and onReimer (1979 and 1985). EB = electron beam, BSE = backscatteredelectron.

FIG. 2 Two explanations for the formation of electron backscatter-ing patterns: (a) Two-event “diffraction model”: A=wide-angle scat-tering event, B=diffraction in exit Bragg planes. (b) Model where thewide-angle event C is modulated by channeling in and channeling out.EB = electron beam.

EBEB

EBSP

EBSPRocking

EB

EBBSE detector

EBSP

(a) (b)

(a) (b)

C

A

S S

B

Description of the “Channeling in and Channelingout” Model for Electron Backscattering Patterns

It is argued above that the diffuse scattering and dif-fraction processes in the two-event “diffraction model”for EBSP are so closely interrelated that for all practicalpurposes these must be regarded as being a single combinedprocess (Fig. 2b). There are three ways in which this ideacan be made to appear as being reasonable:

First is by analogue with the way in which an atomemits either an Auger electron or a characteristic x-rayquantum following the creation of a vacancy in an innershell. As is the case here, this might appear at first sightto take place in two separate steps: first, the vacancy inthe lower level is filled by an electron from a higherlevel; second, the energy so released then gives rise to theemission of either an x-ray quantum from said atom orof an Auger electron from a third level; however, in fact,these steps occur as a single process. In the same way, thescattering and diffraction steps shown in Figure 2a mustbe replaced by the single combined process shown inFigure 2b.

Second is to accept the consequences of reciprocity inthe simplest possible way and to say that the direction intowhich the electron is scattered by a wide-angle event ismodulated directly by the exit Bragg planes. Thus, it ismore likely to excite a type-1 Bloch wave in the exit Braggplanes than a type-2; or, as described by Reimer (1994):“…scattering is more likely to occur into a favorable direc-tion than into an unfavorable one.”

A third possibility was suggested by Batson (privatecommunication 1999) based on recoil effects of the scat-tering atom in the crystal. In the simplest case when anelectron is scattered by an atom in a gas, the scatteringatom does acquire a small recoil velocity as a result of thescattering event. This recoil can occur equally in anydirection, so the scattering is diffuse. However, if theatom is in a crystal then the recoil that it can experienceis modified by the other atoms to which it is coupled inthe crystal lattice (directionally modified effective mass),and this may in turn affect the deflection angle of a scat-tered electron.

According to the “channeling in and channeling out”model for EBSP, a significant fraction of the electrons thatare scattered from the crystal with essentially no energy loss(“reflected elastic peak”) will contain EBSP information,thus explaining the observed sharpness of the lines andbands of contrast in the EBSP.

Contributions of the Slower BackscatteredElectrons and Secondary Electrons to the Forma-tion of Electron Channeling Patterns

It will be noticed that there will be a departure from rec-iprocity between ECP and EBSP involving the slower BSEand SE from the specimen. For the electron paths to be truly

370 Scanning Vol. 21, 6 (1999)

reversible (as reciprocity requires) there must be zeroenergy loss. This is satisfied very nearly by the electronsin the reflected elastic peak, but not for BSE that have beenscattered many times in the specimen or by the SE. Theseslower electrons can, however, contribute usefully to theformation of ECP, as the following argument shows.

FIG. 3 (a) Type-1 and (b) type-2 Bloch wave intensities in a simplecubic lattice according to the latest terminology (modified fromHashimoto et al. 1962).

FIG. 4 Wide-angle scattering of an incident electron immediatelyon entering a solid specimens: (a) with a deflection greater than a rightangle; (b) the same but smaller than a right angle; (c), (d) imaginghigh-Z inclusions in a low-Z target at high resolution by the backscat-tered electron method. Abbreviations as in Figure 1.

(a)

EB BSE EB

Reflecting planes

(a) Type-1 wave: (b) Type-2 wave:

BSE

EB BSE EB BSE

(b)

(c) (d)

O.C. Wells: Electron backscattering patterns 371

Figure 4a shows an electron scattered immediatelythrough more than a right angle and in the right direc-tion to enter the collector directly. As argued above, thiscontributes usefully to the ECP because the probabilityof such an event is modulated by the direction of theincident electrons relative to the Bragg planes. Fur-thermore, since such an electron will suffer only a smallloss of energy, it can be reversed in direction to con-tribute toward the reciprocal relationship between EBSPand ECP.

Figure 4b shows an electron scattered immediatelythrough less than a right angle. This is equivalent to tiltingthe sample through that same angle. Both the BSE and SEcoefficients are therefore increased. Therefore, while thedeflected primary will not enter the collector directly, it ismore likely to give rise to a slower BSE or SE that mightdo so. Thus it can be expected that some of the slower BSE(and SE excited by them) will contain useful ECP infor-mation, provided that the incident electron was scatteredby a wide-angle event immediately after entering the spec-imen; however, the paths of these electrons cannot bereversed.

Figure 4c and d shows situations that are similar in someways to the generation of an ECP. Here, small high-Zinclusions in a low-Z target (either in vertical planes or assmall high-Z particles) are being imaged at high resolutionby the BSE method (Ogura et al. 1990, Wells and Nacuc-chi 1992). The similarity lies in the fact that in both casesthe image contrast is being caused by a wide-angle scat-tering event almost immediately after the electron enters thespecimen. It is to be expected that the faster BSE that arescattered directly into the detector in the manner shown inFigure 4a should contain high-resolution information. Thisargument shows that the slower BSE (and the SE that areexcited by them) might contain high-resolution informa-tion also.

Conclusion and Acknowledgments

I would like to thank the many people who have dis-cussed this problem with me since I first became uneasywith the diffraction model for the formation of EBSP.In particular, I would like to thank P.Batson, D.J.Din-gley, A.Eades, J .J .Friel , P.Ingram, D.C.Joy,J.R.Michael, S.J.Pennycook, and L.Reimer for helpfuldiscussions.

Of necessity, the discussion here has been simplified. Forexample, no mention is made of questions involving excessand defect bands. In the early drafts, the “channeling in andchanneling out” model for EBSP was referred to as “thesingle-event model” because Figure 2b certainly makes itlook as if only a single event is occurring. However, thiswas changed to reflect more closely the importance of thechanneling process.

Likewise, with reference to the fact that Kikuchi lines inthe TEM and EBSP in the SEM are not explained in pre-cisely the same way, Pennycook wrote:

“How about: Kikuchi lines are essentially different. ECPand EBSP can be explained on the basis of elastic scat-tering only (propagation/channelling to an atom site,high angle scattering, and propagation/channelling outof the crystal). Kikuchi lines formed at low angles in theTEM require in addition an inelastic scattering event tofill in some intensity between the Bragg spots.”

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